Problem: Simplify to lowest terms. $\dfrac{78}{104}$
There are several ways to tackle this problem. What is the greatest common factor (GCD) of 78 and 104? $78 = 2\cdot3\cdot13$ $104 = 2\cdot2\cdot2\cdot13$ $\mbox{GCD}(78, 104) = 2\cdot13 = 26$ $\dfrac{78}{104} = \dfrac{3 \cdot 26}{ 4\cdot 26}$ $\hphantom{\dfrac{78}{104}} = \dfrac{3}{4} \cdot \dfrac{26}{26}$ $\hphantom{\dfrac{78}{104}} = \dfrac{3}{4} \cdot 1$ $\hphantom{\dfrac{78}{104}} = \dfrac{3}{4}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{78}{104}= \dfrac{2\cdot39}{2\cdot52}= \dfrac{2\cdot 13\cdot3}{2\cdot 13\cdot4}= \dfrac{3}{4}$